Too bad there are no entrepreneurs left in the USA. This is an enterprise that could have been presented to the banks as a way to recoup their losses; by allowing rental companies to use their marketing and profit expertise.
The Gubmint has no clue how to turn these lemons into lemonade.
I propose the trade down program. If you are going under and the bank is going to take your house, you have the option to trade your house for a smaller one that the bank owns.
Your mortgage goes down, and you get to stay in a house. And while the bank is carrying a higher value property, it’s better than carrying two.